相关论文: Surfaces in 4-manifolds: Addendum

This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.

We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…

The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface in X and an unknotted projective plane in a 4-sphere. This…

This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.

We give a short proof of Ahlfors' theorem on covering surfaces.

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the…

We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.

This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…

We modify the proof of the disc embedding theorem for $4$-manifolds, which appeared as Theorem 5.1A in the book "Topology of 4-manifolds" by Freedman and Quinn, in order to construct geometrically dual spheres. These were claimed in the…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

In this note we extend a theorem from [13] about uniform circle random coverings

This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.

We prove the long-standing Montesinos conjecture that any closed oriented PL 4-manifold M is a simple covering of S^4 branched over a locally flat surface (cf [J M Montesinos, 4-manifolds, 3-fold covering spaces and ribbons, Trans. Amer.…

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

We prove that every quaternionic-contact structure can be embedded in a quaternionic manifold and define a second fundamental form for a such embedding.